{
  "abstract": "Motivated by prescribed Chern scalar curvature problems in complex geometry, we study the equation $Δ_{\\mathbb S^{N-1}}V+λ(e^V-1)=0$ with $λ>0$ on spheres. For $N\\ge4$ and $λ>2(N-2)$ with $λ\\ne2N$, we prove the existence of a nonconstant smooth solution that is axially symmetric and symmetric about the equator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28520",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxuan Li"
    },
    {
      "name": "Qiang Niu"
    },
    {
      "name": "Wubin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpvgm0avqzw1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28520",
  "fulltext_url": null,
  "id": "cpvgm0avqzw1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28520",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223087196",
  "pdf_url": "https://arxiv.org/pdf/2610.28520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpvgm0avqzw1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The $λ>0$ case for $Δu=λ-c e^u$ type equation on high dimensional spheres",
  "title_text": "The λ>0 case for Δu=λ−c e^u type equation on high dimensional spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/cpvgm0avqzw1v",
  "venue": "arXiv",
  "versions": []
}